S is generally used for linear motion, and d is used for vertical linear motion.

Strictly speaking, distance refers to the length of the shortest connection between two points in space at the same time. The nature of the shortest connection depends on the nature of the space where the distance is located. In the straight space in classical physics, it is a straight line, but in a curved space, it can be a curve.

Its application:

The concept of distance is not exactly the same as the module (or magnitude) of displacement. Since displacement is the vector difference between the positions of the same object (referred to as a particle under particle mechanics) at different times (the start and end of motion), the length of the connection between the positions corresponding to its module is long.

Because the displacement is related to different reference systems, and different reference systems may correspond to different states, the problem is that the distance between two points in the coordinate space that is not at the same moment will change; also That is to say, the displacement magnitude of the same physical process is different for different reference systems.

In the real world, the distance between points is determined. For example, Beijing and London are separated by eight time zones. However, if the sun is used as the reference system, an object will experience eight hours. Moving from the longitude of Beijing to the accuracy of London, the magnitude of the lateral displacement of the object is zero.